The damage of the engineering structures caused by scour leads to considerable economical and envi-ronmental losses. The local flow modification and its changes in time during the floods, as well as local geological conditions, as riverbed layering, type and the shape of the structure are the reasons of the in-creased value of the scour depth. The difference in stratification of the riverbed near structures can be one of the reasons of abutment failure because of the scour formation. Although the problem is very topi-cal, the scour at stratified riverbed conditions at the abutments has not been studied wellThe differential equation of the equilibrium for bed sediment movement in clear-water is used and a method for scour calculation in time at abutments is elaborated. The method is confirmed by test results. When the first layer of the bed model is scoured out, the process is continuing in the next layer, but under new hydraulics parameters. Local velocity at the abutments is decreasing in time, at steady flow, but critical one is increasing or decreasing depending on the grain size diameter in the layer. Scour depth, lo-cal and critical velocities development in time under different open-flow conditions, contraction rate of the flow, thickness and sequence of the layers, as well comparison with tests, are presented in Figures.